Global Finance

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Interest Rate Risk Management Using Income and Duration Gap Analysis in Banks-

An Empirical Study

Omid Sharifi 1 , Mehdi Saeidi

2 and Hadi Saeidi

3

1 DBA, Department of Business Administration, AMU, U.P., India

2 Labor inspector of the Department of Cooperatives, Labour and Social Welfare, North Khorasan,

Shirvan 3 Young Researchers and Elite Club, Quchan Branch, Islamic Azad University, Quchan, Iran

ABSTRACT

Banks play a pivotal role in the economic growth and development of countries, primarily through the

diversification of risk for both themselves and other economic agents. Interest rate risk is regarded as one

of the most prominent financial risks faced by a bank. As mainly mentioned by many authors in

professional literature displays, the income and duration gap analysis are considered the most commonly

used IRR measurement tool implicated by banks. This paper examined the different techniques adopted

by banking industry for managing their interest rate risk. To achieve the objectives of the study data has

been collected from secondary sources i.e., from Books, journals and online publications, identified

various risks faced by the banks, Interest Rate Risk types and measure of interest rate risk and managing

net interest income derived by maturity and Duration gap analysis techniques. Finally it can be concluded

that the banks should take risk more consciously, anticipates adverse changes and hedges accordingly, it

becomes a source of competitive advantage, and efficient management of the banking industry.

KEYWORDS: Banking risk, Interest Rate Risk, Interest Rate Risk Management, Gab Analysis

1 Corresponding Author

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INTRODUCTION

Banks can be described as intermediaries

between lenders and borrowers. For competitive

reasons, banks may be obliged to accept client

funds with varying maturities that could

potentially alter the structure of the balance sheet

to an interest rate sensitive position (UBS, 1987:

37). Interest rate risk stems from assets and

liabilities maturing at different times, and

(according to SARB, 2000: 113) can be

encompassed in three elements, namely “the

margin between the rates earned on assets and

paid on liabilities, the reprising potential of assets

and liabilities at different points in time, resulting

in mismatches in various time bands between

assets, liabilities and derivatives, and, finally, the

period during which these mismatches persist”.

Interest rate risk can most aptly be illustrated by

describing the maturity structure of a bank’s

assets and liabilities. Banks are usually described

as being asset or liability sensitive with regard to

the maturity structure of their portfolio. An asset

sensitive bank has a long funded book, whereby

short term assets are funded by long term

liabilities. Should the bank witness a falling

interest rate scenario, the reinvestment of these

assets may be attained at rates that are lower than

the existing rate payments on liabilities.

Obviously, if rates interest rates rise the bank will

prosper under its asset sensitive portfolio (UBS,

1987: 13). Alternatively, a liability sensitive bank

has a short funded book, whereby long term

assets are funded by short term liabilities. Interest

rate risk occurs because liabilities need to be

rolled over until assets become available to repay

the liabilities. In a rising interest rate scenario,

the rollover of the liabilities may occur at a rate

that is greater (more expensive) than the rate

earned on assets, affording a squeeze on bank

interest rate margins. Obviously, if the bank is

faced with a falling interest rate scenario it will

prosper from a liability sensitive portfolio (UBS,

1987: 13). Faure (2002: 134) recognizes that

banks can theoretically avoid interest rate risk by

perfectly matching assets and liabilities “in terms

of currency [term to maturity], and have the rates

on both sides fixed or floating, and thus enjoy a

fixed margin.” If a positive sloping (or normal)

yield curve is assumed, an ideal portfolio can be

constructed for both a falling and rising interest

rate environment. During falling interest rates,

the most beneficial portfolio would be to have all

liabilities short with floating rates and assets long

with fixed rates (and vice versa for a rising

interest rate environment). Faure (2002)

recognizes that in reality the ideal portfolio

construct can be dependent on variables such as

bank competition as well as the requirements of

clients, investors and stakeholders, all of which

may affect the composition of the balance sheet.

Thus, banks are naturally exposed to interest rate

risk as they have a large variety of assets and

liabilities that differ in term to maturity and

reprising frequency. Interest rate risk is viewed

by many as one of the most significant risks of a

bank. A large portion of private banks’ revenue

stems from net interest income that is generated

from the difference between various assets and

liabilities that are held in the balance sheet.

According to SARB (2007a: 103), interest

income and interest expense represented 7% and

4.7% of total assets respectively (and therefore an

interest margin of 2.3%) for the 12 month

average at December 2005. Interest rate risk has

its importance in affecting the amount of interest

income and interest expenditure of a bank.

PURPOSE OF THE RESEARCH

Risk management is defined by Dickson (1989:

18) in Valsamakis et al (1992: 13) as “the

identification, analysis and economic control of

those risks which threaten the assets or earning

capacity of an organisation.” As such the

management of risk has, explicitly or implicitly,

become part of a strategic component of the

modern organisation’s survival and development

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(Waring and Glendon, 1998: 3) Interest rate risk

is regarded by a number of authors such as

Heffernan (1996), Bessis (2002) and Sinkey

(2002) as one of the most prominent financial

risks faced by a bank. Interest rate risk

management is by no means a new trend in

banking activities. Williamson (2008, 14)

described that interest rate risk arises when there

are mismatches between maturity of bank’s

assets and liabilities. In a bank where long-term

liabilities are used to fund short term assets,

interest rate risk exposes itself as a reinvested

risk due to assets mature before liabilities. If the

interest rate falls, the reinvestment of those assets

will be at a lower rate than the existing rate

payments on liabilities. Obviously, the bank will

earn profit from the risk as the interest rate

increases. Heffernan (1996: 189) and Gup and

Kolari (2005: 121) describe gap analysis as the

easiest and most commonly used interest rate risk

measurement tool. Therefore, it is necessary that

measurement of interest rate risk should be

considered by Banks. So, regarding to

international banking rule (Basel Committee

Accords) and RBI guidelines the investigation of

risk analysis and risk management in banking

sector is being most important.

OBJECTIVES THE STUDY:

The following are the objectives of the study.

- To identify the risks faced by the banking

industry.

- To determine types of Interest Rate Risk

-To examine the techniques adopted by

banking industry for managing their interest

rate risk.

- To derived Measure of interest rate risk and

managing net interest income by maturity

and Duration gap analysis techniques.

RESEARCH METHODOLOGY

This paper is theoretical modal based on the

extensive research for which the secondary

source of information has gathered. data has

been collected from secondary sources i.e.,

from Books, journals and online publications,

identified various risks faced by the banks,

Interest Rate Risk types and measure of

interest rate risk and managing net interest

income derived by maturity and Duration gap

analysis techniques.

LITERATURE REVIEW

Interest rate risk is regarded by a number of

authors such as Heffernan (1996), Bessis

(2002) and Sinkey (2002) as one of the most

prominent financial risks faced by a bank.

Interest rate risk management is by no means

a new trend in banking activities. Prior to the

early 1970s South African banks focussed

primarily on the asset side of their balance

sheet, as the liability side was regarded as a

‘given’. This, of course, was not detrimental

because interest rates were relatively stable

(often under deposit rate control) and

monetary policy was based on interest rate

targeting resulting in a stable funding cost

environment. The hedging of interest rate

risk under these market conditions was

achieved by manipulating the banks’ balance

sheets to be either short- or long-funded

during the interest rate cycle (UBS, 1987:

38). The early 1970s, however, brought a

change to stable market conditions: the UBS

(1987: 38) recognises “the oil crisis, large

international capital flows, significant

inflation differentials between countries, an

unstable exchange rate system and a large

increase in the debt of the public sector” as

contributory factors. Moreover, the 1980s

provided no more stability than the previous

decade: the traditional banking cartel

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arrangement was disbanded resulting in

increased competition, interest was payable

on certain current accounts for the first time,

the transition of the central bank policy to a

cash reserve system induced an increased

interest rate volatility and the creation of new

complex financial instruments and services

which were primarily driven by market rates

all added to the increased market instability

(UBS, 1987: 38). This resulted in investors’

and borrowers’ preferences shifting to

variable rate deposits and loans in an attempt

to avoid sharp interest rate fluctuations. In

essence, the banks’ cost of funds had now

switched from no or low interest to high

yielding rate-sensitive accounts. The banks’

liabilities became far more susceptible to

interest rates and prompted the inclusion of

effective interest rate risk management for

bank liabilities (UBS, 1987: 39). Blue and

Hedberg (2001) in Mahshid and Naji (2001:

1) comment that the evolution in the financial

sector over the last twenty years has resulted

in intricate balance sheet structures

containing complicated derivative

instruments. Pyle (1997: 2) recognises that

leveraging inherent in various interest rate

derivatives provides an accelerated risk

exposure for hedgers, while acknowledging

that it is not necessarily the derivative

instruments that cause this increased risk per

se, but rather ineffective risk management. At

this point, it is important to note that bank

risk is managed by a number of internal

committees. One such committee is the asset

and liability committee (ALCO), whose role

is manage a bank's interest rate risk by

primarily focusing on the type, volume and

maturity structure of financial instruments in

changing economic environments (Meek,

1987: 5). The ALCO is responsible for the

formulation of the basic borrowing and

lending strategy, and therefore affects all

bank divisions.

BANKING RISKS

Pyle (1997) indicated that banking risks

include four major sources: Market risk

(including interest rate, exchange rate, and

equity and commodity prices), Credit risk,

Operational risk, Performance risk. The

classification seems to be adequate, but it still

doesn’t have the existence of environmental

risks which combine national laws, legal

structure and the differences concerning the

laws between two countries. Another

classification is from Greuning & Bratanovic

(2009), which is more adequate and

comprehensive than the first conception.

According to the authors, banking business

these days has to face three main crucial

issues: financial, operational, and

environmental risks (see Table 1).

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Table 1: Categories of Banking Risks

Financial Risks Operational Risks Environmental Risk

Balance Sheet structure Internal fund Country and political

risks

Earning and income statement

structure

External fraud Macroeconomic policy

Capital adequacy Employments practices and workplace

safety

Financial infrastructure

Credit Clients, products, and business services Legal infrastructure

Liquidity Damage to physical assets Banking crisis and

contagion

Market Business disruption and system failures

Interest rate -- --

Currency -- --

Source: Greuning & Bratanovic 2009, 3-4

As can be seen, a bank is facing a large number of different kinds of risks due to the complexity of

economy. The banking risks can damage banks’ operations, and banking systems or even the whole

economy. Significantly, they are drastically increasing; in both quantity and complex degrees and their

devastating level is different over the periods depending on their individual characteristics.

INTEREST RATE RISK

In figure 1 has shows interest rate risk in this research:

Figure 1: Interest Rate Risk types

The Re-pricing risk, as well as the reinvested

risk, presents a possibility of mismatching of

assets and liabilities at different times (maturity)

and rates (floating rate). (Basel Committee on

Banking Supervision 2004, 5)

The Basic Risk occurs when there is imperfect

correlation of bases, such as U.S Treasury Bill

rate and London Interbank Offered Rate, on

which earnings on assets and costs on liabilities

are based. Because the bank’s asset and

liabilities are dependent on different bases, if

there is a move on each base in different

directions, the bank will suffer unexpected

changes in revenues and expenses. (Basel

Committee on Banking Supervision 2004, 5)

The Yield Curve Risk is caused by the changes

in the slope and the shape of yield curve, which

refers to the relationship between short-term and

long-term interest rates gained by bank. (Basel

Committee on Banking Supervision 2004, 5)

The Embedded option Risk, as its name, is the

risk caused by options that are embedded in

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bank’s assets and liabilities. Unless adequately

managed implications, the products with

optionality features can be a source for

signification risk for the banks offering them.

(Basel Committee on Banking Supervision

2004, 6)

INTEREST RATE RISK MANAGEMENT

Apparently, banking sector is exactly known to

be the risky sector in the world economy due to

their business’s nature relating to money. They

play a role as intermediaries who distribute cash

flow between parties in the financial market or

even as parties who are considered as investors.

Accepting risk is a normal business principle of

banking and interest rate risk does not stay out

of the line. It seems to be an important source of

profitability and economics value for

commercial banks; meanwhile it can also be a

source of significant threats if the level of yield

is excessive. Accordingly, keeping interest rate

at a prudent level is necessary to retain the safety

and soundness of banking institutions which

pose to the efficient management of interest rate.

(cf. Trading and Capital-Markets Activities

manual 1998) .IRR management is a set of

policies and procedures implemented by banking

institutions with the purpose of identifying,

measuring and monitoring the movement of

interest rate to restrain and avoid the unfavorable

risk’s impacts and may be making use of

fluctuation of yield curve to obtain new

opportunities (Raghavan 2003, 842). Under the

distinguishing economic factors of different

countries where commercial banks have their

business, the methods in which interest rates are

controlled in order to maintain its IRR’s

exposure within authorized level are varied.

These methods are depending upon the

complexity and the nature of its structures and

activities, and IRR exposure (Trading and

Capital-Markets Activities manual 1998).

However, it seems to be difficult to assess the

management of interest rate risk without the

general standards. The sound IRR management

conducted by Basel Committee on Banking

Supervision –the principles for the Management

and Supervision of Interest Rate Risk can be a

response and a reliable source on which analysts

may rely to evaluate the activities of bank’s

managing risk of interest rate (Basel Committee

on Banking Supervision 2004). In the guideline,

the committee offers four basic elements

embedded into the management of IRR (see

Figure 3).

Figure 3: Sound IRR management practice

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In order to adapt the approaches and standards

for an efficient IRR management suggested by

Basel Committee, it is required for banks to rely

on an internal committee which is in charge of

the duty of managing interest rate risk (Greuning

& Bratanovic 2009, 277; Bessis 2002, 131). The

asset and liability committee (ALCO) is

responsible for its mentioned duty. It is engaged

in restructuring balance sheet – adjusting

component accounts in assets and liabilities. It

helps to maintain stabilization and maximizes

the interest merge of the interest paid to

mobilized fund in bank’s liabilities and interest

income on its asset, simultaneously to comply

the liquidity required by central bank (Greuning

& Bratanovic 2009, 278). In the following,

ALCO will present its structure (including its

decision making process, broad of senior

managers, reporting), internal and external

policies, and its function containing IRR

measuring, simulating, and hedging.

INTEREST RATE RISK MEASUREMENT

The IRR measurement is the first step in the

process where the risk is analyzed, and the

measurement methods are chosen properly to

quantify the IRR exposure, plan solving tactics,

diminish risk and ensure the targeted income of

banking institutions or even obtain new

opportunities (Trading and Capital-Markets

Activities manual 1998, 6-7). For measuring

IRR, banks use a variety of methods such as

maturity structure analysis, income gap analysis,

duration gap analysis, balance sheet and net

interest income projection, risk-return analysis,

ratio analysis. Each method has its sophistication

and complexity aiming to the similar purpose of

quantifying bank’s IRR profile, which is suitable

to each banking institution. (Williamson (2008,

23)

As mainly mentioned by many authors in

professional literature displays, the income and

duration gap analysis are considered the most

commonly used IRR measurement tool

implicated by banks (Greuning & Bratanovic

2009, 282-286; Choudhry 2011, 186; Bank of

Jamaica 2005, 9-10; Williamson 2008, 87-96).

- Income Gap Analysis: is a measuring model

which analyzes re-pricing gap of cash flow

between the interest revenues earned on assets

and interest expenses paid on liability in a

particular period of time (Greuning &

Bratanovic 2009, 282). If the interest return of

asset and interest expense of liability re-prices as

there is any change in rate, they will be

respectively considered as asset or liability

sensitive to the interest rate (Choudhry 2011,

186). In addition, in gap model, the rate sensitive

asset (RSA) and rate sensitive liability (RSL) are

usually defined to re-price in specific periods

such as 0 – 30 days, 31 – 90 days, 91 – 181 days

and etc (Williamson 2008, 89). In order to

recognize a bank of RSA or RSL styles, the

interest sensitive ratio in equation 1 (see

Appendix 2) will indicate, in which if the ratio is

larger than 1 the bank will be considered as RSA

bank and vice versa (Oracle Finance 2008, 4).

The gap, as its name, represents the imbalance

between the rate sensitive asset and liability,

which directly affects the net interest income

(NII) of the bank. With any maturity time of

bank’s assets and liabilities, it is able to protect

its earning and economics value against the

unfavorable changes of the interest rate by

maintaining the balance of rate sensitive asset

and liability, which means RSA is equal to RSL.

However, there are many reasons that make the

balance hardly appear accidentally, thus the gap

is created. Equations 2 and 3 (see Appendix 2)

will present the relationship between the balance

of rate sensitive asset and liability to bank’s NII

(see Table 5). (Williamson 2008, 87-89.)

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Table 5: The alternative consequence of gap, interest rate changes and net interest income

Gap Change in interest

rates

Change in net interest

income

Positive RSA > RSL Increase Increase

Positive RSA > RSL Decrease Decrease

Negative RSA < RSL Increase Decrease

Negative RSA < RSL Decrease Increase

Zero RSA = RSL Increase No change

Zero RSA = RSL Decrease No change

The equation 3 reveals the effect of Gap on the

interest income of a bank. They are assumed to

exist in the three cases. Firstly, in the zero gap,

the rate sensitive asset and liability are equal;

therefore, the NII will not affect the increase or

decrease of the interest rate. Secondly, when the

gap is positive, the rate sensitive asset is larger

than the rate sensitive liability, so the interest

income will be larger than the interest expense

as a rise of interest rate and vice versa. Finally,

when the gap is negative, the RSA will be lower

than the RSL. If the interest rate increases, the

bank will suffer a loss as the interest expense is

larger than the interest income and vice versa.

These can be summarized in Table 5 that shows

the relationship between the gaps and the

changes in interest rate and net interest income.

(cf. Oracle Finance 2008, 4.)

Theoretically, if a bank can predict the

fluctuation of IRR, and then recognize the

balance sheet re-pricing (asset or liability

sensitive to interest rate), it will restructure the

balance sheet in a way based on the positive or

negative gaps to obtain the advantage of rise in

NII. However, practically the probability of

predicting the correct interest rate fluctuation is

low. However, this will cause a low level of

interest margins. (Greuning & Bratanovic 2009,

283). From the advantages of the method,

Greuning & Bratanovic (2009, 284) stated that

the gap analysis method would give a single

numeric result on which managers could rely to

produce straightforward target for hedging IRR.

However, this method also supposes to some

disadvantages. Firstly, it focuses on the current

interest sensitivity of asset and liability which

ignore the mismatch of asset and liability in

medium and long term position. Secondly, the

method overlooks the time position of asset and

liability in a range of maturity. They are

assumed to mature or re-price at the same time

although almost liabilities re-price at the end of

period while assets may re-price at the

beginning. In addition, the income gap cannot

show changes in the market value of bank’s net

worth because its calculation is based on the

interest income and cost. Due to the mentioned

limitations of gap analysis, the duration gap

analysis will be described to fill the limits in the

next part. (Figure 4) (Greuning & Bratanovic

2009, 284; Bank of Jamaica 2005, 9-10.)

Maturity Gap Method – Mathematical

Expressions:

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Figure4: Income gap analysis equation (Oracle Finance 2008, 4)

Duration-gap analysis:

The duration gap is known as the mismatch of

asset and liability’s timing, so duration gap

analysis is a method of measuring the changes of

market value of banking institutions’ net worth

(cash flow of asset and liability) due to the

fluctuation of interest rates. It is defined as a

measurement of average lifetime of asset and

liability in time periods when assets are mature

Gap Ratio = RSAs / RSLs

NII = Gap r

Where

NII = Cheng In Net Income

r = Cheng In Interest Rate

NII = Earning Assets NIM

NII = Earning Assets NIM C

Where

C = %chang in NIM

Since, NII = Gap r

Gap r =Earning assets NII C

GAP =

Where

Earning Assets = total Assets of the Bank

NII = net Interest Margin

C = Acceptable change in NIM

r = expect change in interest Rates

RSG = RSAs – RSLs

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to be returned and liabilities to be paid.

(Greuning & Bratanovic 2009, 286-287.) In

order to calculate the duration gap, it initially

computes the average duration of each asset and

liability which is respectively the average time

to recover the invested capital and the average

time needed to repay the mobilized fund (Oracle

Finance 2008, 4). The equations expressing the

duration gap and the relationship between

duration gap and the net worth of bank are

mentioned in Appendix 3. In order to manage

IRR, banking institution can base on equation 4

to adjust the balance sheet position to make the

duration gap nearly equal zero so that any

change of interest rate has no impact on the

value of bank’s equity, or in other words the

bank becomes immunized against IRR.

However, in practice, banks have obligation to

ensure the liquidity to sudden fund withdrawal

and maintain a specific of level of fund

reservation so that assets always have greater

value than liabilities. A result is derived from

equation 4 in order to attain zero duration gap,

and the average duration of liability has to be

larger than that of asset. (Oracle Finance 2008,

4) The duration gap, along with interest rate

fluctuation, directly conducts the gain and loss

of bank’s net worth. According to equation 5,

the net worth movement due to the changes in

duration gap and interest rate will be displayed

in Table 6. Although measuring the duration

gap is more complicated than the income gap

model because more numbers and complex

calculation process and some of asset and

liability have a specific pattern which may not

be well-defined, the method provides a

comprehensive measure of interest rate risk for

the total portfolio rather than individual account

measurement as income gap method. In

addition, the duration gap analysis method also

indicates the time value of money (Greuning &

Bratanovic 2009, 287; Oracle finance 2008, 5).

Table 6: Duration-gap analysis

Duration gap Change in interest rate Change in net worth

Positive Increase Decrease

Positive Decrease Increase

Negative Increase Increase

Negative Decrease Decrease

Zero Increase No change

Zero Decrease No change

Both the method income and duration gap

analysis are assumed to have problems that meet

the customer’s default risk. Besides, to the

duration gap analysis, the interest rate for all

maturities are pretended to be similar, so the

yield curve is considered to be flat. However,

the yield curves are not flat in practice because

they are volatile. Therefore, the duration gap

works well with the small changes in interest

rate. With the great change, banking managers

should observe the slope of the yield curve as

the changes in the rate and then take the

information into account when measuring the

risk. (Greuning & Bratanovic 2009; Oracle

finance 2008)

However, these mentioned limitations of the

income gap and duration gap analysis do not

prevent ALCO senior managers from

implementation because they provide simple

frameworks for the first assessment of interest

rate risk. Depending on the scope of banking

institutions and their business activities and

specific time, ALCO senior managers can use

only the income gap or duration gap analysis, or

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reach the more sophisticated approaches of IRR

measurement such as risk-return analysis.

(Williamson 2008, 92)

Duration-GAP Method – Mathematical

Expressions:

Duration-GAP Analysis It is another measure of

interest rate risk and managing net interest

income derived by taking into consideration all

individual cash inflows and outflows. The

duration gap is often cited along with the

maturity gap as one of the most common interest

rate sensitivity measurement tools. The duration

of a stock is expressed algebraically by the UBS

(1988: 43) as:

1)

Where

D = DURATION

t = time period (length of time of cash flow)

n = number of periods of time of final maturity

=total cash flow (interest and/ or principal

repayment) at time period t

r = yield to maturity

Summation sign

The UBS (1987: 43) identifies the denominator

as “the present value of the entire cash flow

from the stock, while the numerator is the

present value of that part of the cash flow due in

period t. By definition, therefore, the term in

parenthesis gives the proportion of the entire

cash flow from the stock that is due in period t”.

The UBS (1987: 47) as well as Gup and Kolari

(2005: 135 – 138) identify that due to the linear

relationship duration provides between a change

in the market

Yield and the price of a sock over the maturity

scale, the principals of duration can be used as

an interest rate sensitivity measure. Houpt and

Embersit (1991: 637) in Gup and Kolari (2005:

137) identify that modified duration has the

ability to “reflect an instrument’s discrete

compounding

of interest; duration measures the instrument’s

price volatility to changes in market yields”. The

authors familiarise modified duration as the

measure of the price elasticity of a financial

instrument with regard to interest rate changes.

Modified duration is expressed algebraically by

Houpt and Embersit (1991: 637) in Gup and

Kolari (2005: 137) as:

2) Modified duration =

Where

R = per period rate of return of the instrument

C = number of time per period that interest is

compounded

Alternatively, this relationship between the

instrument’s price sensitivity, modified duration

and changes in the rate of interest is expressed

by Houpt and Embersit (1991: 637) in Gup and

Kolari (2005: 137) as:

3) Percentage change in price = -

Modified

duration

Houpt and Embersit (1991: 637) in Gup and

Kolari (2005: 137) maintain that since duration

provides a standard measure of price sensitivity

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for a variety of financial instruments, the

duration of an entire portfolio (e.g. a bank’s

portfolio) can be calculated as the weighted

average of the portfolio’s components. From this

analysis, the duration of the firm’s net worth can

be defined as the weighted average of its assets

and liabilities. The weighted averages of assets,

liabilities and off-balance sheet items’ estimated

duration will yield a measure of interest rate risk

exposure. Duration is value and time weighted

measure of maturity of all cash flows and

represents the average time needed to recover

the invested funds. Duration analysis can be

viewed as the elasticity of the market value of an

instrument with respect to interest rate. Duration

gap (DGAP) reflects the differences in the

timing of asset and liability cash flows and given

by, DGAP = DA - u DL. Where DA is the

average duration of the assets, DL is the average

duration of liabilities, and u is the

liabilities/assets ratio. When interest rate

increases by comparable amounts, the market

value of assets decrease more than that of

liabilities resulting in the decrease in the market

value of equities and expected net-interest

income and vice versa. (Cumming and Beverly,

2001)

Using the Duration analysis to assess the sensitivity of the market value of assets and liabilities:

4)

Where,

= Duration Gap / duration of Surplus

= Duration of assets

= Duration of liabilities

A = Assets

L = Liabilities

S = Surplus / Gap

Substituting L = A – S in the above eqn. We get

5)

When there is a market fluctuation,

6)

Where,

MV = Change in the market value

D = duration of assets or Liabilities

r = Change in the interest rate

r = Current interest rate

MV = Market Value

Then,

New MV = Current MV + MV

× S = ( × A) – ( ×L)

= + (A / S) - )

MAGNT Research Report (ISSN. 1444-8939) Vol.2 (7). PP: 3058-3071

(DOI: dx.doi.org/14.9831/1444-8939.2014/2-7/MAGNT.129)

7)

CONCLUSION:

It is obvious that the interest rate changes affect

the profitability and economic values of bank in

various forms and different sources which are

the components conducting the interest rates

offered by lenders such as inflation and default

(credit) risk premium, maturity and liquidity

premium (Keown & Martin 2006). In addition,

the interest rate risk significantly relates to

environmental risks such as changes in

monetary, fiscal and economic policies of

Governments or Central Bank with the aim of

managing the national financial market. The

Central Bank, for instance, announces an

increase reserve ratio; after that the lending rates

are also adjusted to compensate for the increase

in costs caused by changes of reserve

requirement. Hence, interest rate risk

management is a rising crucial issue that every

bank under its distinct financial situation,

national economy, economic policies and etc.

would have its efficient strategies and process in

order to minimize the risk and maximize the

profit and organizational value. In the next

chapter interest rate risk management will be

discussed. Briefly, interest rate risk is one of the

financial risks assumed by banks. The risk

occurs when there is a mismatch between re-

pricing assets and liabilities. It is formed in four

types – basis, yield curve, re-pricing and

optional risks. Interest rate risk has significant

impact on banks’ short- and long-term value

(earning and economic value), especially

commercial banks whose main revenues rely on

investment, and mobilizing and lending

activities. Due to its impacts, the interest rate

risk management should be considered in proper

manner. The well-established structure of the

risk management unit, the unit’s personnel, a set

of policies concerning to the risk, the reporting

of the risk measurement, simulation, hedging,

risk and return, and the risk limits should be

taken into account. In addition, the crucial role

of regulatory environment imposed by the

Central Bank in managing interest rate risk

cannot be ignored.

REFERENCES

BESSIS, J., 2002. Risk management in banking

(2e). Singapore: John Wiley and Sons.

Choudhry, M. 2011. Introduction to Banking:

Liquidity Risk and Asset-liability Management.

Wiley, USA.

FAURE, A.P., 2002. Getting to grips with

private sector banking. Cape Town: QUOIN

Institute (Pty) Limited.

Greuning, H & Bratanovic, S. 2009. Analyzing

Banking Risk: A Framework for Assessing

Corporate Governance and Risk Management.

3rd Edition. The World Bank. Washington,

USA.

GUP, B.E. and KOLARI, J.W., 2005.

Commercial banking: the management of risk

(3e). New Jersey: John Wiley and Sons.

HEFFERNAN, S., 1996. Modern banking in

theory and practice. New York: John Wiley and

Sons.

Keown, A & Martin, J & Petty, W & Scott, D.

2006. Foundation of Finance: The Logic and

Practice of Financial Management. 5th Ed.

Pearson Prentice Hall. USA.

MAHSHID, D. and NAJI, M.R., 2003.

Managing interest-rate risk – a case study of

four Swedish savings banks. Masters Thesis.

Höstterminen: School of Economics and

Commercial Law, Göteborg University.

MEEK P., 1987. Banks as managers of risk. in:

Falkena, H.B., Kok, W.J. and Meijer, J.H. (eds).

The dynamics of the South African financial

MAGNT Research Report (ISSN. 1444-8939) Vol.2 (7). PP: 3058-3071

(DOI: dx.doi.org/14.9831/1444-8939.2014/2-7/MAGNT.129)

system: financial risk management.

Johannesburg: Macmillan Press.

Oralce Financial Services. 2008. Asset and

Liability Management: Overview. Oracle

Corporation, Accessed 28.09.2012.

PYLE, D.H., 1997: Bank risk management:

theory. Research program in finance: working

papers. University of California, Berkeley.

Raghavan, R. 2003. Risk Management in Banks.

Accessed 18.09.2012.

http://www.icai.org/resource_file/11490p841-

851.pdf

SARB, 2007a. Bank Supervision Department:

Annual report 2005. [Online]. Available:

http://www.reservebank.co.za [Accessed 8

March 2007].

SARB, 2007b. Banks Act, 1990. [Online].

Available: http://www.reservebank.co.za

[Accessed 22 March 2007].

SARB, 2007c. Bank Supervision Department:

bank DI 900 returns. [Online]. Available:

http://www.reservebank.co.za [Accessed 17 July

2007].

SARB, 2007d. Statistical and economic

information. [Online]. Available:

http://www.reservebank.co.za [Accessed 14

September 2007].

SINKEY, J.F.Jr., 2002. Commercial bank

financial management: in the financial-services

industry (6e). New Jersey: Prentice Hall.

VALSAMAKIS, A.C. VIVIAN, R.W. and DU

TOIT, G.S., 1992. The theories and principles of

risk management. Durban: Butterworths.

VALSAMAKIS, A.C. VIVIAN, R.W. and DU

TOIT, G.S., 1999. Risk management (2e).

Sandton: Heienemann Higher and Futher

Education (Pty) Ltd.

WARING, A.E. and GLENDON, A.I., 1998.

Managing risk: critical issues for survival and

success into the 21st century. Toronto:

International Thomson Business Press.

Williamson,G., 2008. Interest rate risk

management: a case study Of GBS mutual bank.

A Master thesis, Rhodes University.